Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

David Jensen, Sam Payne

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We develop a framework to apply tropical and nonarchimedean analytic methods to multiplication maps for linear series on algebraic curves, studying degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a new proof of the Gieseker–Petri theorem, including an explicit tropical criterion for a curve over a valued field to be Gieseker–Petri general.

Original languageEnglish
Pages (from-to)2043-2066
Number of pages24
JournalAlgebra and Number Theory
Volume8
Issue number9
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
©2014 Mathematical Sciences Publishers.

Keywords

  • Chain of loops
  • Gieseker–Petri theorem
  • Multiplication maps
  • Nonarchimedean geometry
  • Poincaré–Lelong
  • Tropical Brill–Noether theory
  • Tropical independence

ASJC Scopus subject areas

  • Algebra and Number Theory

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